Question

A random sample of 13 students were asked how long it took them to complete a certain exam. The mean length of time was 107.3 minutes, with a standard deviation of 82.5 minutes. Find the lower bound of the 90% confidence interval for the true mean length of time it would take for all students to complete the exam.

Round to one decimal place (for example: 108.1). Write only a number as your answer. Do not write any units.

Answer 1

Given that,

= 107.3

s =82.5

n = 13

Degrees of freedom = df = n - 1 = 13- 1 = 12

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

= 0.10

t ,df = t0.10,12 = 1.356 ( using student t table)

Margin of error = E = t,df * (s /n)

=1.356 * (82.5 / 13) = 31.03

The 90% confidence interval estimate of the population mean is,

- E

107.3 - 31.03

76.27

lower bound=76.3